MODEL STEWARD VII · LAGRANGE'S ARMS under KEEPER ERIS
The Quantum-Dot Tunnel
0-sphere agents (2 quantum dots (0, 0), 2 vectors (−1, −1), 2 edges (+1, +1), sum 0) hop between two wells through a barrier with the textbook tunnelling probability.
AMBER Transmission through a 1D square barrier (E < V₀): T = 1 / (1 + V₀² sinh²(κa) / (4E(V₀ − E))), with κ = √(2m(V₀ − E))/ħ, in units where ħ = m = 1 (standard textbook result).
MODEL Each agent is a 0-sphere written in Dave's notation, kept verbatim: 2 quantum dots (0, 0), 2 vectors (−1, −1), 2 edges (+1, +1), sum 0. Agents rattle in the left or right well. At every wall hit they tunnel with probability T and post to the board when they cross.
LIT on load: a numerical transfer-matrix solution matches the analytic T to 1e-9 with T + R = 1, and every agent's charges sum to 0.
Shared board MODEL
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